TSTP Solution File: SEV197^5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEV197^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n028.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Tue Jul 19 17:35:37 EDT 2022

% Result   : Theorem 0.20s 0.42s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   12
% Syntax   : Number of formulae    :  127 (  62 unt;  11 typ;   0 def)
%            Number of atoms       :  576 ( 370 equ;   0 cnn)
%            Maximal formula atoms :    8 (   4 avg)
%            Number of connectives : 1113 ( 241   ~; 181   |;  39   &; 631   @)
%                                         (   0 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   3 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   55 (  55   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  10 usr;   9 con; 0-2 aty)
%            Number of variables   :  346 (   0   ^ 346   !;   0   ?; 346   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_iS,type,
    iS: $tType ).

thf(tp_c0,type,
    c0: iS ).

thf(tp_cP,type,
    cP: iS > iS > iS ).

thf(tp_sK1_Xx,type,
    sK1_Xx: iS ).

thf(tp_sK2_SY16,type,
    sK2_SY16: iS ).

thf(tp_sK3_SY19,type,
    sK3_SY19: iS ).

thf(tp_sK4_SY21,type,
    sK4_SY21: iS ).

thf(tp_sK5_Xx,type,
    sK5_Xx: iS ).

thf(tp_sK6_SY22,type,
    sK6_SY22: iS ).

thf(tp_sK7_Xx,type,
    sK7_Xx: ( iS > $o ) > iS ).

thf(tp_sK8_SY23,type,
    sK8_SY23: ( iS > $o ) > iS ).

thf(1,conjecture,
    ( ( ! [Xx: iS,Xy: iS] :
          ( ( cP @ Xx @ Xy )
         != c0 )
      & ! [Xx: iS,Xy: iS,Xu: iS,Xv: iS] :
          ( ( ( cP @ Xx @ Xu )
            = ( cP @ Xy @ Xv ) )
         => ( ( Xx = Xy )
            & ( Xu = Xv ) ) )
      & ! [X: iS > $o] :
          ( ( ( X @ c0 )
            & ! [Xx: iS,Xy: iS] :
                ( ( ( X @ Xx )
                  & ( X @ Xy ) )
               => ( X @ ( cP @ Xx @ Xy ) ) ) )
         => ! [Xx: iS] : ( X @ Xx ) ) )
   => ( ! [Xx: iS,Xy: iS,Xu: iS,Xv: iS] :
          ( ( ( cP @ Xx @ Xu )
            = ( cP @ Xy @ Xv ) )
         => ( ( Xx = Xy )
            & ( Xu = Xv ) ) )
      & ! [Xx: iS,Xy: iS] :
          ( ( cP @ Xx @ Xy )
         != c0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cS_ALG02_pme) ).

thf(2,negated_conjecture,
    ( ( ( ! [Xx: iS,Xy: iS] :
            ( ( cP @ Xx @ Xy )
           != c0 )
        & ! [Xx: iS,Xy: iS,Xu: iS,Xv: iS] :
            ( ( ( cP @ Xx @ Xu )
              = ( cP @ Xy @ Xv ) )
           => ( ( Xx = Xy )
              & ( Xu = Xv ) ) )
        & ! [X: iS > $o] :
            ( ( ( X @ c0 )
              & ! [Xx: iS,Xy: iS] :
                  ( ( ( X @ Xx )
                    & ( X @ Xy ) )
                 => ( X @ ( cP @ Xx @ Xy ) ) ) )
           => ! [Xx: iS] : ( X @ Xx ) ) )
     => ( ! [Xx: iS,Xy: iS,Xu: iS,Xv: iS] :
            ( ( ( cP @ Xx @ Xu )
              = ( cP @ Xy @ Xv ) )
           => ( ( Xx = Xy )
              & ( Xu = Xv ) ) )
        & ! [Xx: iS,Xy: iS] :
            ( ( cP @ Xx @ Xy )
           != c0 ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ( ! [Xx: iS,Xy: iS] :
            ( ( cP @ Xx @ Xy )
           != c0 )
        & ! [Xx: iS,Xy: iS,Xu: iS,Xv: iS] :
            ( ( ( cP @ Xx @ Xu )
              = ( cP @ Xy @ Xv ) )
           => ( ( Xx = Xy )
              & ( Xu = Xv ) ) )
        & ! [X: iS > $o] :
            ( ( ( X @ c0 )
              & ! [Xx: iS,Xy: iS] :
                  ( ( ( X @ Xx )
                    & ( X @ Xy ) )
                 => ( X @ ( cP @ Xx @ Xy ) ) ) )
           => ! [Xx: iS] : ( X @ Xx ) ) )
     => ( ! [Xx: iS,Xy: iS,Xu: iS,Xv: iS] :
            ( ( ( cP @ Xx @ Xu )
              = ( cP @ Xy @ Xv ) )
           => ( ( Xx = Xy )
              & ( Xu = Xv ) ) )
        & ! [Xx: iS,Xy: iS] :
            ( ( cP @ Xx @ Xy )
           != c0 ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ! [Xx: iS,Xy: iS] :
          ( ( cP @ Xx @ Xy )
         != c0 ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(5,plain,
    ( ( ! [Xx: iS,Xy: iS,Xu: iS,Xv: iS] :
          ( ( ( cP @ Xx @ Xu )
            = ( cP @ Xy @ Xv ) )
         => ( ( Xx = Xy )
            & ( Xu = Xv ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(6,plain,
    ( ( ! [X: iS > $o] :
          ( ( ( X @ c0 )
            & ! [Xx: iS,Xy: iS] :
                ( ( ( X @ Xx )
                  & ( X @ Xy ) )
               => ( X @ ( cP @ Xx @ Xy ) ) ) )
         => ! [Xx: iS] : ( X @ Xx ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(7,plain,
    ( ( ! [Xx: iS,Xy: iS,Xu: iS,Xv: iS] :
          ( ( ( cP @ Xx @ Xu )
            = ( cP @ Xy @ Xv ) )
         => ( ( Xx = Xy )
            & ( Xu = Xv ) ) )
      & ! [Xx: iS,Xy: iS] :
          ( ( cP @ Xx @ Xy )
         != c0 ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(8,plain,
    ( ( ! [Xx: iS,Xy: iS,Xu: iS,Xv: iS] :
          ( ( ( cP @ Xx @ Xu )
            = ( cP @ Xy @ Xv ) )
         => ( ( Xx = Xy )
            & ( Xu = Xv ) ) ) )
    = $false ),
    inference(split_conjecture,[split_conjecture(split,[])],[7]) ).

thf(9,plain,
    ( ( ! [Xx: iS,Xy: iS] :
          ( ( cP @ Xx @ Xy )
         != c0 ) )
    = $false ),
    inference(split_conjecture,[split_conjecture(split,[])],[7]) ).

thf(10,plain,
    ( ( ~ ! [Xx: iS,Xy: iS,Xu: iS,Xv: iS] :
            ( ( ( cP @ Xx @ Xu )
              = ( cP @ Xy @ Xv ) )
           => ( ( Xx = Xy )
              & ( Xu = Xv ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[8]) ).

thf(11,plain,
    ( ( ~ ! [Xx: iS,Xy: iS] :
            ( ( cP @ Xx @ Xy )
           != c0 ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[9]) ).

thf(12,plain,
    ( ( ( ( cP @ sK1_Xx @ sK3_SY19 )
        = ( cP @ sK2_SY16 @ sK4_SY21 ) )
      & ( ( sK1_Xx != sK2_SY16 )
        | ( sK3_SY19 != sK4_SY21 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[10]) ).

thf(13,plain,
    ( ( ( cP @ sK5_Xx @ sK6_SY22 )
      = c0 )
    = $true ),
    inference(extcnf_combined,[status(esa)],[11]) ).

thf(14,plain,
    ( ( ! [Xx: iS,Xy: iS] :
          ( ( cP @ Xx @ Xy )
         != c0 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[4]) ).

thf(15,plain,
    ( ( ! [Xx: iS,Xy: iS] :
          ( ( ! [Xu: iS,Xv: iS] :
                ( ( cP @ Xx @ Xu )
               != ( cP @ Xy @ Xv ) )
            | ( Xx = Xy ) )
          & ! [Xu: iS,Xv: iS] :
              ( ( ( cP @ Xx @ Xu )
               != ( cP @ Xy @ Xv ) )
              | ( Xu = Xv ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5]) ).

thf(16,plain,
    ( ( ! [X: iS > $o] :
          ( ( ( X @ ( sK7_Xx @ X ) )
            & ( X @ ( sK8_SY23 @ X ) )
            & ~ ( X @ ( cP @ ( sK7_Xx @ X ) @ ( sK8_SY23 @ X ) ) ) )
          | ~ ( X @ c0 )
          | ! [Xx: iS] : ( X @ Xx ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[6]) ).

thf(17,plain,
    ( ( ! [X: iS > $o] :
          ( ( ( X @ ( sK7_Xx @ X ) )
            & ( X @ ( sK8_SY23 @ X ) )
            & ~ ( X @ ( cP @ ( sK7_Xx @ X ) @ ( sK8_SY23 @ X ) ) ) )
          | ~ ( X @ c0 )
          | ! [Xx: iS] : ( X @ Xx ) ) )
    = $true ),
    inference(copy,[status(thm)],[16]) ).

thf(18,plain,
    ( ( ! [Xx: iS,Xy: iS] :
          ( ( ! [Xu: iS,Xv: iS] :
                ( ( cP @ Xx @ Xu )
               != ( cP @ Xy @ Xv ) )
            | ( Xx = Xy ) )
          & ! [Xu: iS,Xv: iS] :
              ( ( ( cP @ Xx @ Xu )
               != ( cP @ Xy @ Xv ) )
              | ( Xu = Xv ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[15]) ).

thf(19,plain,
    ( ( ! [Xx: iS,Xy: iS] :
          ( ( cP @ Xx @ Xy )
         != c0 ) )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(20,plain,
    ( ( ( ( cP @ sK1_Xx @ sK3_SY19 )
        = ( cP @ sK2_SY16 @ sK4_SY21 ) )
      & ( ( sK1_Xx != sK2_SY16 )
        | ( sK3_SY19 != sK4_SY21 ) ) )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

thf(21,plain,
    ( ( ~ ( ( ( cP @ sK1_Xx @ sK3_SY19 )
           != ( cP @ sK2_SY16 @ sK4_SY21 ) )
          | ~ ( ( sK1_Xx != sK2_SY16 )
              | ( sK3_SY19 != sK4_SY21 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[20]) ).

thf(22,plain,
    ( ( ! [SX0: iS > $o] :
          ( ~ ( ~ ~ ( ~ ( SX0 @ ( sK7_Xx @ SX0 ) )
                    | ~ ( SX0 @ ( sK8_SY23 @ SX0 ) ) )
              | ~ ~ ( SX0 @ ( cP @ ( sK7_Xx @ SX0 ) @ ( sK8_SY23 @ SX0 ) ) ) )
          | ~ ( SX0 @ c0 )
          | ! [SX1: iS] : ( SX0 @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[17]) ).

thf(23,plain,
    ( ( ! [SX0: iS,SX1: iS] :
          ~ ( ~ ( ! [SX2: iS,SX3: iS] :
                    ( ( cP @ SX0 @ SX2 )
                   != ( cP @ SX1 @ SX3 ) )
                | ( SX0 = SX1 ) )
            | ~ ! [SX2: iS,SX3: iS] :
                  ( ( ( cP @ SX0 @ SX2 )
                   != ( cP @ SX1 @ SX3 ) )
                  | ( SX2 = SX3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[18]) ).

thf(24,plain,
    ! [SV1: iS] :
      ( ( ! [SY24: iS] :
            ( ( cP @ SV1 @ SY24 )
           != c0 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[19]) ).

thf(25,plain,
    ( ( ( ( cP @ sK1_Xx @ sK3_SY19 )
       != ( cP @ sK2_SY16 @ sK4_SY21 ) )
      | ~ ( ( sK1_Xx != sK2_SY16 )
          | ( sK3_SY19 != sK4_SY21 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[21]) ).

thf(26,plain,
    ! [SV2: iS > $o] :
      ( ( ~ ( ~ ~ ( ~ ( SV2 @ ( sK7_Xx @ SV2 ) )
                  | ~ ( SV2 @ ( sK8_SY23 @ SV2 ) ) )
            | ~ ~ ( SV2 @ ( cP @ ( sK7_Xx @ SV2 ) @ ( sK8_SY23 @ SV2 ) ) ) )
        | ~ ( SV2 @ c0 )
        | ! [SY25: iS] : ( SV2 @ SY25 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[22]) ).

thf(27,plain,
    ! [SV3: iS] :
      ( ( ! [SY26: iS] :
            ~ ( ~ ( ! [SY27: iS,SY28: iS] :
                      ( ( cP @ SV3 @ SY27 )
                     != ( cP @ SY26 @ SY28 ) )
                  | ( SV3 = SY26 ) )
              | ~ ! [SY29: iS,SY30: iS] :
                    ( ( ( cP @ SV3 @ SY29 )
                     != ( cP @ SY26 @ SY30 ) )
                    | ( SY29 = SY30 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[23]) ).

thf(28,plain,
    ! [SV4: iS,SV1: iS] :
      ( ( ( ( cP @ SV1 @ SV4 )
         != c0 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[24]) ).

thf(29,plain,
    ( ( ( ( cP @ sK1_Xx @ sK3_SY19 )
       != ( cP @ sK2_SY16 @ sK4_SY21 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[25]) ).

thf(30,plain,
    ( ( ~ ( ( sK1_Xx != sK2_SY16 )
          | ( sK3_SY19 != sK4_SY21 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[25]) ).

thf(31,plain,
    ! [SV2: iS > $o] :
      ( ( ( ~ ( ~ ~ ( ~ ( SV2 @ ( sK7_Xx @ SV2 ) )
                    | ~ ( SV2 @ ( sK8_SY23 @ SV2 ) ) )
              | ~ ~ ( SV2 @ ( cP @ ( sK7_Xx @ SV2 ) @ ( sK8_SY23 @ SV2 ) ) ) )
          | ~ ( SV2 @ c0 ) )
        = $true )
      | ( ( ! [SY25: iS] : ( SV2 @ SY25 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[26]) ).

thf(32,plain,
    ! [SV5: iS,SV3: iS] :
      ( ( ~ ( ~ ( ! [SY31: iS,SY32: iS] :
                    ( ( cP @ SV3 @ SY31 )
                   != ( cP @ SV5 @ SY32 ) )
                | ( SV3 = SV5 ) )
            | ~ ! [SY33: iS,SY34: iS] :
                  ( ( ( cP @ SV3 @ SY33 )
                   != ( cP @ SV5 @ SY34 ) )
                  | ( SY33 = SY34 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[27]) ).

thf(33,plain,
    ! [SV4: iS,SV1: iS] :
      ( ( ( cP @ SV1 @ SV4 )
        = c0 )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[28]) ).

thf(34,plain,
    ( ( ( cP @ sK1_Xx @ sK3_SY19 )
      = ( cP @ sK2_SY16 @ sK4_SY21 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[29]) ).

thf(35,plain,
    ( ( ( sK1_Xx != sK2_SY16 )
      | ( sK3_SY19 != sK4_SY21 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[30]) ).

thf(36,plain,
    ! [SV2: iS > $o] :
      ( ( ( ~ ( ~ ~ ( ~ ( SV2 @ ( sK7_Xx @ SV2 ) )
                    | ~ ( SV2 @ ( sK8_SY23 @ SV2 ) ) )
              | ~ ~ ( SV2 @ ( cP @ ( sK7_Xx @ SV2 ) @ ( sK8_SY23 @ SV2 ) ) ) ) )
        = $true )
      | ( ( ~ ( SV2 @ c0 ) )
        = $true )
      | ( ( ! [SY25: iS] : ( SV2 @ SY25 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[31]) ).

thf(37,plain,
    ! [SV5: iS,SV3: iS] :
      ( ( ~ ( ! [SY31: iS,SY32: iS] :
                ( ( cP @ SV3 @ SY31 )
               != ( cP @ SV5 @ SY32 ) )
            | ( SV3 = SV5 ) )
        | ~ ! [SY33: iS,SY34: iS] :
              ( ( ( cP @ SV3 @ SY33 )
               != ( cP @ SV5 @ SY34 ) )
              | ( SY33 = SY34 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[32]) ).

thf(38,plain,
    ( ( ( ( sK1_Xx != sK2_SY16 ) )
      = $true )
    | ( ( ( sK3_SY19 != sK4_SY21 ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[35]) ).

thf(39,plain,
    ! [SV2: iS > $o] :
      ( ( ( ~ ~ ( ~ ( SV2 @ ( sK7_Xx @ SV2 ) )
                | ~ ( SV2 @ ( sK8_SY23 @ SV2 ) ) )
          | ~ ~ ( SV2 @ ( cP @ ( sK7_Xx @ SV2 ) @ ( sK8_SY23 @ SV2 ) ) ) )
        = $false )
      | ( ( ~ ( SV2 @ c0 ) )
        = $true )
      | ( ( ! [SY25: iS] : ( SV2 @ SY25 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[36]) ).

thf(40,plain,
    ! [SV5: iS,SV3: iS] :
      ( ( ~ ( ! [SY31: iS,SY32: iS] :
                ( ( cP @ SV3 @ SY31 )
               != ( cP @ SV5 @ SY32 ) )
            | ( SV3 = SV5 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[37]) ).

thf(41,plain,
    ! [SV5: iS,SV3: iS] :
      ( ( ~ ! [SY33: iS,SY34: iS] :
              ( ( ( cP @ SV3 @ SY33 )
               != ( cP @ SV5 @ SY34 ) )
              | ( SY33 = SY34 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[37]) ).

thf(42,plain,
    ( ( ( sK1_Xx = sK2_SY16 )
      = $false )
    | ( ( ( sK3_SY19 != sK4_SY21 ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[38]) ).

thf(43,plain,
    ! [SV2: iS > $o] :
      ( ( ( ~ ~ ( ~ ( SV2 @ ( sK7_Xx @ SV2 ) )
                | ~ ( SV2 @ ( sK8_SY23 @ SV2 ) ) ) )
        = $false )
      | ( ( ~ ( SV2 @ c0 ) )
        = $true )
      | ( ( ! [SY25: iS] : ( SV2 @ SY25 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[39]) ).

thf(44,plain,
    ! [SV2: iS > $o] :
      ( ( ( ~ ~ ( SV2 @ ( cP @ ( sK7_Xx @ SV2 ) @ ( sK8_SY23 @ SV2 ) ) ) )
        = $false )
      | ( ( ~ ( SV2 @ c0 ) )
        = $true )
      | ( ( ! [SY25: iS] : ( SV2 @ SY25 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[39]) ).

thf(45,plain,
    ! [SV5: iS,SV3: iS] :
      ( ( ! [SY31: iS,SY32: iS] :
            ( ( cP @ SV3 @ SY31 )
           != ( cP @ SV5 @ SY32 ) )
        | ( SV3 = SV5 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[40]) ).

thf(46,plain,
    ! [SV5: iS,SV3: iS] :
      ( ( ! [SY33: iS,SY34: iS] :
            ( ( ( cP @ SV3 @ SY33 )
             != ( cP @ SV5 @ SY34 ) )
            | ( SY33 = SY34 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[41]) ).

thf(47,plain,
    ( ( ( sK3_SY19 = sK4_SY21 )
      = $false )
    | ( ( sK1_Xx = sK2_SY16 )
      = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[42]) ).

thf(48,plain,
    ! [SV2: iS > $o] :
      ( ( ( ~ ( ~ ( SV2 @ ( sK7_Xx @ SV2 ) )
              | ~ ( SV2 @ ( sK8_SY23 @ SV2 ) ) ) )
        = $true )
      | ( ( ~ ( SV2 @ c0 ) )
        = $true )
      | ( ( ! [SY25: iS] : ( SV2 @ SY25 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[43]) ).

thf(49,plain,
    ! [SV2: iS > $o] :
      ( ( ( ~ ( SV2 @ ( cP @ ( sK7_Xx @ SV2 ) @ ( sK8_SY23 @ SV2 ) ) ) )
        = $true )
      | ( ( ~ ( SV2 @ c0 ) )
        = $true )
      | ( ( ! [SY25: iS] : ( SV2 @ SY25 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[44]) ).

thf(50,plain,
    ! [SV5: iS,SV3: iS] :
      ( ( ( ! [SY31: iS,SY32: iS] :
              ( ( cP @ SV3 @ SY31 )
             != ( cP @ SV5 @ SY32 ) ) )
        = $true )
      | ( ( SV3 = SV5 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[45]) ).

thf(51,plain,
    ! [SV5: iS,SV6: iS,SV3: iS] :
      ( ( ! [SY35: iS] :
            ( ( ( cP @ SV3 @ SV6 )
             != ( cP @ SV5 @ SY35 ) )
            | ( SV6 = SY35 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[46]) ).

thf(52,plain,
    ! [SV2: iS > $o] :
      ( ( ( ~ ( SV2 @ ( sK7_Xx @ SV2 ) )
          | ~ ( SV2 @ ( sK8_SY23 @ SV2 ) ) )
        = $false )
      | ( ( ~ ( SV2 @ c0 ) )
        = $true )
      | ( ( ! [SY25: iS] : ( SV2 @ SY25 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[48]) ).

thf(53,plain,
    ! [SV2: iS > $o] :
      ( ( ( SV2 @ ( cP @ ( sK7_Xx @ SV2 ) @ ( sK8_SY23 @ SV2 ) ) )
        = $false )
      | ( ( ~ ( SV2 @ c0 ) )
        = $true )
      | ( ( ! [SY25: iS] : ( SV2 @ SY25 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[49]) ).

thf(54,plain,
    ! [SV5: iS,SV7: iS,SV3: iS] :
      ( ( ( ! [SY36: iS] :
              ( ( cP @ SV3 @ SV7 )
             != ( cP @ SV5 @ SY36 ) ) )
        = $true )
      | ( ( SV3 = SV5 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[50]) ).

thf(55,plain,
    ! [SV8: iS,SV5: iS,SV6: iS,SV3: iS] :
      ( ( ( ( cP @ SV3 @ SV6 )
         != ( cP @ SV5 @ SV8 ) )
        | ( SV6 = SV8 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[51]) ).

thf(56,plain,
    ! [SV2: iS > $o] :
      ( ( ( ~ ( SV2 @ ( sK7_Xx @ SV2 ) ) )
        = $false )
      | ( ( ~ ( SV2 @ c0 ) )
        = $true )
      | ( ( ! [SY25: iS] : ( SV2 @ SY25 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[52]) ).

thf(57,plain,
    ! [SV2: iS > $o] :
      ( ( ( ~ ( SV2 @ ( sK8_SY23 @ SV2 ) ) )
        = $false )
      | ( ( ~ ( SV2 @ c0 ) )
        = $true )
      | ( ( ! [SY25: iS] : ( SV2 @ SY25 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[52]) ).

thf(58,plain,
    ! [SV2: iS > $o] :
      ( ( ( SV2 @ c0 )
        = $false )
      | ( ( SV2 @ ( cP @ ( sK7_Xx @ SV2 ) @ ( sK8_SY23 @ SV2 ) ) )
        = $false )
      | ( ( ! [SY25: iS] : ( SV2 @ SY25 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[53]) ).

thf(59,plain,
    ! [SV9: iS,SV5: iS,SV7: iS,SV3: iS] :
      ( ( ( ( ( cP @ SV3 @ SV7 )
           != ( cP @ SV5 @ SV9 ) ) )
        = $true )
      | ( ( SV3 = SV5 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[54]) ).

thf(60,plain,
    ! [SV8: iS,SV5: iS,SV6: iS,SV3: iS] :
      ( ( ( ( ( cP @ SV3 @ SV6 )
           != ( cP @ SV5 @ SV8 ) ) )
        = $true )
      | ( ( SV6 = SV8 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[55]) ).

thf(61,plain,
    ! [SV2: iS > $o] :
      ( ( ( SV2 @ ( sK7_Xx @ SV2 ) )
        = $true )
      | ( ( ~ ( SV2 @ c0 ) )
        = $true )
      | ( ( ! [SY25: iS] : ( SV2 @ SY25 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[56]) ).

thf(62,plain,
    ! [SV2: iS > $o] :
      ( ( ( SV2 @ ( sK8_SY23 @ SV2 ) )
        = $true )
      | ( ( ~ ( SV2 @ c0 ) )
        = $true )
      | ( ( ! [SY25: iS] : ( SV2 @ SY25 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[57]) ).

thf(63,plain,
    ! [SV10: iS,SV2: iS > $o] :
      ( ( ( SV2 @ SV10 )
        = $true )
      | ( ( SV2 @ ( cP @ ( sK7_Xx @ SV2 ) @ ( sK8_SY23 @ SV2 ) ) )
        = $false )
      | ( ( SV2 @ c0 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[58]) ).

thf(64,plain,
    ! [SV9: iS,SV5: iS,SV7: iS,SV3: iS] :
      ( ( ( ( cP @ SV3 @ SV7 )
          = ( cP @ SV5 @ SV9 ) )
        = $false )
      | ( ( SV3 = SV5 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[59]) ).

thf(65,plain,
    ! [SV8: iS,SV5: iS,SV6: iS,SV3: iS] :
      ( ( ( ( cP @ SV3 @ SV6 )
          = ( cP @ SV5 @ SV8 ) )
        = $false )
      | ( ( SV6 = SV8 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[60]) ).

thf(66,plain,
    ! [SV2: iS > $o] :
      ( ( ( SV2 @ c0 )
        = $false )
      | ( ( SV2 @ ( sK7_Xx @ SV2 ) )
        = $true )
      | ( ( ! [SY25: iS] : ( SV2 @ SY25 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[61]) ).

thf(67,plain,
    ! [SV2: iS > $o] :
      ( ( ( SV2 @ c0 )
        = $false )
      | ( ( SV2 @ ( sK8_SY23 @ SV2 ) )
        = $true )
      | ( ( ! [SY25: iS] : ( SV2 @ SY25 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[62]) ).

thf(68,plain,
    ! [SV11: iS,SV2: iS > $o] :
      ( ( ( SV2 @ SV11 )
        = $true )
      | ( ( SV2 @ ( sK7_Xx @ SV2 ) )
        = $true )
      | ( ( SV2 @ c0 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[66]) ).

thf(69,plain,
    ! [SV12: iS,SV2: iS > $o] :
      ( ( ( SV2 @ SV12 )
        = $true )
      | ( ( SV2 @ ( sK8_SY23 @ SV2 ) )
        = $true )
      | ( ( SV2 @ c0 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[67]) ).

thf(70,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[33,69,68,65,64,63,47,34]) ).

thf(71,plain,
    ( ( ! [X: iS > $o] :
          ( ( ( X @ ( sK7_Xx @ X ) )
            & ( X @ ( sK8_SY23 @ X ) )
            & ~ ( X @ ( cP @ ( sK7_Xx @ X ) @ ( sK8_SY23 @ X ) ) ) )
          | ~ ( X @ c0 )
          | ! [Xx: iS] : ( X @ Xx ) ) )
    = $true ),
    inference(copy,[status(thm)],[16]) ).

thf(72,plain,
    ( ( ! [Xx: iS,Xy: iS] :
          ( ( ! [Xu: iS,Xv: iS] :
                ( ( cP @ Xx @ Xu )
               != ( cP @ Xy @ Xv ) )
            | ( Xx = Xy ) )
          & ! [Xu: iS,Xv: iS] :
              ( ( ( cP @ Xx @ Xu )
               != ( cP @ Xy @ Xv ) )
              | ( Xu = Xv ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[15]) ).

thf(73,plain,
    ( ( ! [Xx: iS,Xy: iS] :
          ( ( cP @ Xx @ Xy )
         != c0 ) )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(74,plain,
    ( ( ( cP @ sK5_Xx @ sK6_SY22 )
      = c0 )
    = $true ),
    inference(copy,[status(thm)],[13]) ).

thf(75,plain,
    ( ( ! [SX0: iS,SX1: iS] :
          ~ ( ~ ( ! [SX2: iS,SX3: iS] :
                    ( ( cP @ SX0 @ SX2 )
                   != ( cP @ SX1 @ SX3 ) )
                | ( SX0 = SX1 ) )
            | ~ ! [SX2: iS,SX3: iS] :
                  ( ( ( cP @ SX0 @ SX2 )
                   != ( cP @ SX1 @ SX3 ) )
                  | ( SX2 = SX3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[72]) ).

thf(76,plain,
    ( ( ! [SX0: iS > $o] :
          ( ~ ( ~ ~ ( ~ ( SX0 @ ( sK7_Xx @ SX0 ) )
                    | ~ ( SX0 @ ( sK8_SY23 @ SX0 ) ) )
              | ~ ~ ( SX0 @ ( cP @ ( sK7_Xx @ SX0 ) @ ( sK8_SY23 @ SX0 ) ) ) )
          | ~ ( SX0 @ c0 )
          | ! [SX1: iS] : ( SX0 @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[71]) ).

thf(77,plain,
    ! [SV13: iS] :
      ( ( ! [SY37: iS] :
            ( ( cP @ SV13 @ SY37 )
           != c0 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[73]) ).

thf(78,plain,
    ! [SV14: iS] :
      ( ( ! [SY38: iS] :
            ~ ( ~ ( ! [SY39: iS,SY40: iS] :
                      ( ( cP @ SV14 @ SY39 )
                     != ( cP @ SY38 @ SY40 ) )
                  | ( SV14 = SY38 ) )
              | ~ ! [SY41: iS,SY42: iS] :
                    ( ( ( cP @ SV14 @ SY41 )
                     != ( cP @ SY38 @ SY42 ) )
                    | ( SY41 = SY42 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[75]) ).

thf(79,plain,
    ! [SV15: iS > $o] :
      ( ( ~ ( ~ ~ ( ~ ( SV15 @ ( sK7_Xx @ SV15 ) )
                  | ~ ( SV15 @ ( sK8_SY23 @ SV15 ) ) )
            | ~ ~ ( SV15 @ ( cP @ ( sK7_Xx @ SV15 ) @ ( sK8_SY23 @ SV15 ) ) ) )
        | ~ ( SV15 @ c0 )
        | ! [SY43: iS] : ( SV15 @ SY43 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[76]) ).

thf(80,plain,
    ! [SV16: iS,SV13: iS] :
      ( ( ( ( cP @ SV13 @ SV16 )
         != c0 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[77]) ).

thf(81,plain,
    ! [SV17: iS,SV14: iS] :
      ( ( ~ ( ~ ( ! [SY44: iS,SY45: iS] :
                    ( ( cP @ SV14 @ SY44 )
                   != ( cP @ SV17 @ SY45 ) )
                | ( SV14 = SV17 ) )
            | ~ ! [SY46: iS,SY47: iS] :
                  ( ( ( cP @ SV14 @ SY46 )
                   != ( cP @ SV17 @ SY47 ) )
                  | ( SY46 = SY47 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[78]) ).

thf(82,plain,
    ! [SV15: iS > $o] :
      ( ( ( ~ ( ~ ~ ( ~ ( SV15 @ ( sK7_Xx @ SV15 ) )
                    | ~ ( SV15 @ ( sK8_SY23 @ SV15 ) ) )
              | ~ ~ ( SV15 @ ( cP @ ( sK7_Xx @ SV15 ) @ ( sK8_SY23 @ SV15 ) ) ) )
          | ~ ( SV15 @ c0 ) )
        = $true )
      | ( ( ! [SY43: iS] : ( SV15 @ SY43 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[79]) ).

thf(83,plain,
    ! [SV16: iS,SV13: iS] :
      ( ( ( cP @ SV13 @ SV16 )
        = c0 )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[80]) ).

thf(84,plain,
    ! [SV17: iS,SV14: iS] :
      ( ( ~ ( ! [SY44: iS,SY45: iS] :
                ( ( cP @ SV14 @ SY44 )
               != ( cP @ SV17 @ SY45 ) )
            | ( SV14 = SV17 ) )
        | ~ ! [SY46: iS,SY47: iS] :
              ( ( ( cP @ SV14 @ SY46 )
               != ( cP @ SV17 @ SY47 ) )
              | ( SY46 = SY47 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[81]) ).

thf(85,plain,
    ! [SV15: iS > $o] :
      ( ( ( ~ ( ~ ~ ( ~ ( SV15 @ ( sK7_Xx @ SV15 ) )
                    | ~ ( SV15 @ ( sK8_SY23 @ SV15 ) ) )
              | ~ ~ ( SV15 @ ( cP @ ( sK7_Xx @ SV15 ) @ ( sK8_SY23 @ SV15 ) ) ) ) )
        = $true )
      | ( ( ~ ( SV15 @ c0 ) )
        = $true )
      | ( ( ! [SY43: iS] : ( SV15 @ SY43 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[82]) ).

thf(86,plain,
    ! [SV17: iS,SV14: iS] :
      ( ( ~ ( ! [SY44: iS,SY45: iS] :
                ( ( cP @ SV14 @ SY44 )
               != ( cP @ SV17 @ SY45 ) )
            | ( SV14 = SV17 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[84]) ).

thf(87,plain,
    ! [SV17: iS,SV14: iS] :
      ( ( ~ ! [SY46: iS,SY47: iS] :
              ( ( ( cP @ SV14 @ SY46 )
               != ( cP @ SV17 @ SY47 ) )
              | ( SY46 = SY47 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[84]) ).

thf(88,plain,
    ! [SV15: iS > $o] :
      ( ( ( ~ ~ ( ~ ( SV15 @ ( sK7_Xx @ SV15 ) )
                | ~ ( SV15 @ ( sK8_SY23 @ SV15 ) ) )
          | ~ ~ ( SV15 @ ( cP @ ( sK7_Xx @ SV15 ) @ ( sK8_SY23 @ SV15 ) ) ) )
        = $false )
      | ( ( ~ ( SV15 @ c0 ) )
        = $true )
      | ( ( ! [SY43: iS] : ( SV15 @ SY43 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[85]) ).

thf(89,plain,
    ! [SV17: iS,SV14: iS] :
      ( ( ! [SY44: iS,SY45: iS] :
            ( ( cP @ SV14 @ SY44 )
           != ( cP @ SV17 @ SY45 ) )
        | ( SV14 = SV17 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[86]) ).

thf(90,plain,
    ! [SV17: iS,SV14: iS] :
      ( ( ! [SY46: iS,SY47: iS] :
            ( ( ( cP @ SV14 @ SY46 )
             != ( cP @ SV17 @ SY47 ) )
            | ( SY46 = SY47 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[87]) ).

thf(91,plain,
    ! [SV15: iS > $o] :
      ( ( ( ~ ~ ( ~ ( SV15 @ ( sK7_Xx @ SV15 ) )
                | ~ ( SV15 @ ( sK8_SY23 @ SV15 ) ) ) )
        = $false )
      | ( ( ~ ( SV15 @ c0 ) )
        = $true )
      | ( ( ! [SY43: iS] : ( SV15 @ SY43 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[88]) ).

thf(92,plain,
    ! [SV15: iS > $o] :
      ( ( ( ~ ~ ( SV15 @ ( cP @ ( sK7_Xx @ SV15 ) @ ( sK8_SY23 @ SV15 ) ) ) )
        = $false )
      | ( ( ~ ( SV15 @ c0 ) )
        = $true )
      | ( ( ! [SY43: iS] : ( SV15 @ SY43 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[88]) ).

thf(93,plain,
    ! [SV17: iS,SV14: iS] :
      ( ( ( ! [SY44: iS,SY45: iS] :
              ( ( cP @ SV14 @ SY44 )
             != ( cP @ SV17 @ SY45 ) ) )
        = $true )
      | ( ( SV14 = SV17 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[89]) ).

thf(94,plain,
    ! [SV17: iS,SV18: iS,SV14: iS] :
      ( ( ! [SY48: iS] :
            ( ( ( cP @ SV14 @ SV18 )
             != ( cP @ SV17 @ SY48 ) )
            | ( SV18 = SY48 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[90]) ).

thf(95,plain,
    ! [SV15: iS > $o] :
      ( ( ( ~ ( ~ ( SV15 @ ( sK7_Xx @ SV15 ) )
              | ~ ( SV15 @ ( sK8_SY23 @ SV15 ) ) ) )
        = $true )
      | ( ( ~ ( SV15 @ c0 ) )
        = $true )
      | ( ( ! [SY43: iS] : ( SV15 @ SY43 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[91]) ).

thf(96,plain,
    ! [SV15: iS > $o] :
      ( ( ( ~ ( SV15 @ ( cP @ ( sK7_Xx @ SV15 ) @ ( sK8_SY23 @ SV15 ) ) ) )
        = $true )
      | ( ( ~ ( SV15 @ c0 ) )
        = $true )
      | ( ( ! [SY43: iS] : ( SV15 @ SY43 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[92]) ).

thf(97,plain,
    ! [SV17: iS,SV19: iS,SV14: iS] :
      ( ( ( ! [SY49: iS] :
              ( ( cP @ SV14 @ SV19 )
             != ( cP @ SV17 @ SY49 ) ) )
        = $true )
      | ( ( SV14 = SV17 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[93]) ).

thf(98,plain,
    ! [SV20: iS,SV17: iS,SV18: iS,SV14: iS] :
      ( ( ( ( cP @ SV14 @ SV18 )
         != ( cP @ SV17 @ SV20 ) )
        | ( SV18 = SV20 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[94]) ).

thf(99,plain,
    ! [SV15: iS > $o] :
      ( ( ( ~ ( SV15 @ ( sK7_Xx @ SV15 ) )
          | ~ ( SV15 @ ( sK8_SY23 @ SV15 ) ) )
        = $false )
      | ( ( ~ ( SV15 @ c0 ) )
        = $true )
      | ( ( ! [SY43: iS] : ( SV15 @ SY43 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[95]) ).

thf(100,plain,
    ! [SV15: iS > $o] :
      ( ( ( SV15 @ ( cP @ ( sK7_Xx @ SV15 ) @ ( sK8_SY23 @ SV15 ) ) )
        = $false )
      | ( ( ~ ( SV15 @ c0 ) )
        = $true )
      | ( ( ! [SY43: iS] : ( SV15 @ SY43 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[96]) ).

thf(101,plain,
    ! [SV21: iS,SV17: iS,SV19: iS,SV14: iS] :
      ( ( ( ( ( cP @ SV14 @ SV19 )
           != ( cP @ SV17 @ SV21 ) ) )
        = $true )
      | ( ( SV14 = SV17 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[97]) ).

thf(102,plain,
    ! [SV20: iS,SV17: iS,SV18: iS,SV14: iS] :
      ( ( ( ( ( cP @ SV14 @ SV18 )
           != ( cP @ SV17 @ SV20 ) ) )
        = $true )
      | ( ( SV18 = SV20 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[98]) ).

thf(103,plain,
    ! [SV15: iS > $o] :
      ( ( ( ~ ( SV15 @ ( sK7_Xx @ SV15 ) ) )
        = $false )
      | ( ( ~ ( SV15 @ c0 ) )
        = $true )
      | ( ( ! [SY43: iS] : ( SV15 @ SY43 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[99]) ).

thf(104,plain,
    ! [SV15: iS > $o] :
      ( ( ( ~ ( SV15 @ ( sK8_SY23 @ SV15 ) ) )
        = $false )
      | ( ( ~ ( SV15 @ c0 ) )
        = $true )
      | ( ( ! [SY43: iS] : ( SV15 @ SY43 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[99]) ).

thf(105,plain,
    ! [SV15: iS > $o] :
      ( ( ( SV15 @ c0 )
        = $false )
      | ( ( SV15 @ ( cP @ ( sK7_Xx @ SV15 ) @ ( sK8_SY23 @ SV15 ) ) )
        = $false )
      | ( ( ! [SY43: iS] : ( SV15 @ SY43 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[100]) ).

thf(106,plain,
    ! [SV21: iS,SV17: iS,SV19: iS,SV14: iS] :
      ( ( ( ( cP @ SV14 @ SV19 )
          = ( cP @ SV17 @ SV21 ) )
        = $false )
      | ( ( SV14 = SV17 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[101]) ).

thf(107,plain,
    ! [SV20: iS,SV17: iS,SV18: iS,SV14: iS] :
      ( ( ( ( cP @ SV14 @ SV18 )
          = ( cP @ SV17 @ SV20 ) )
        = $false )
      | ( ( SV18 = SV20 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[102]) ).

thf(108,plain,
    ! [SV15: iS > $o] :
      ( ( ( SV15 @ ( sK7_Xx @ SV15 ) )
        = $true )
      | ( ( ~ ( SV15 @ c0 ) )
        = $true )
      | ( ( ! [SY43: iS] : ( SV15 @ SY43 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[103]) ).

thf(109,plain,
    ! [SV15: iS > $o] :
      ( ( ( SV15 @ ( sK8_SY23 @ SV15 ) )
        = $true )
      | ( ( ~ ( SV15 @ c0 ) )
        = $true )
      | ( ( ! [SY43: iS] : ( SV15 @ SY43 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[104]) ).

thf(110,plain,
    ! [SV22: iS,SV15: iS > $o] :
      ( ( ( SV15 @ SV22 )
        = $true )
      | ( ( SV15 @ ( cP @ ( sK7_Xx @ SV15 ) @ ( sK8_SY23 @ SV15 ) ) )
        = $false )
      | ( ( SV15 @ c0 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[105]) ).

thf(111,plain,
    ! [SV15: iS > $o] :
      ( ( ( SV15 @ c0 )
        = $false )
      | ( ( SV15 @ ( sK7_Xx @ SV15 ) )
        = $true )
      | ( ( ! [SY43: iS] : ( SV15 @ SY43 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[108]) ).

thf(112,plain,
    ! [SV15: iS > $o] :
      ( ( ( SV15 @ c0 )
        = $false )
      | ( ( SV15 @ ( sK8_SY23 @ SV15 ) )
        = $true )
      | ( ( ! [SY43: iS] : ( SV15 @ SY43 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[109]) ).

thf(113,plain,
    ! [SV23: iS,SV15: iS > $o] :
      ( ( ( SV15 @ SV23 )
        = $true )
      | ( ( SV15 @ ( sK7_Xx @ SV15 ) )
        = $true )
      | ( ( SV15 @ c0 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[111]) ).

thf(114,plain,
    ! [SV24: iS,SV15: iS > $o] :
      ( ( ( SV15 @ SV24 )
        = $true )
      | ( ( SV15 @ ( sK8_SY23 @ SV15 ) )
        = $true )
      | ( ( SV15 @ c0 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[112]) ).

thf(115,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[74,114,113,110,107,106,83]) ).

thf(116,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[115,70]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SEV197^5 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33  % Computer : n028.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Tue Jun 28 00:02:26 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  
% 0.12/0.34   No.of.Axioms: 0
% 0.12/0.34  
% 0.12/0.34   Length.of.Defs: 0
% 0.12/0.34  
% 0.12/0.34   Contains.Choice.Funs: false
% 0.12/0.34  (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)......
% 0.20/0.42  
% 0.20/0.42  ********************************
% 0.20/0.42  *   All subproblems solved!    *
% 0.20/0.42  ********************************
% 0.20/0.42  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:115,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.43  
% 0.20/0.43  %**** Beginning of derivation protocol ****
% 0.20/0.43  % SZS output start CNFRefutation
% See solution above
% 0.20/0.43  
% 0.20/0.43  %**** End of derivation protocol ****
% 0.20/0.43  %**** no. of clauses in derivation: 116 ****
% 0.20/0.43  %**** clause counter: 115 ****
% 0.20/0.43  
% 0.20/0.43  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:115,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------